Concentration-measure theory of waves: new perspectives of the fundamentals of nonequilibrium statistical physics and mesoscopic physics

The foundations of statistical physics are currently under renovations. A number of scenarios for the arising of statistical physics in an individual system has been proposed. However, most studies have focused on equilibrium statistical physics. In this talk, I shall report our recent progress on the fundamentals of nonequilibrium statistical physics. I will show a theory for structures and fluctuations of waves in individual disordered media, using the mathematical tool of the concentration of measure. Applying this theory, we can see how the elementary nonequilibrium process of diffusion can arise from a single scattering state of wave equation, without the canonical hypothesis of ensembles. Furthermore, fluctuations associated with the change in incoming waves exhibit a new kind of universalities, which does not exist in conventional mesoscopic fluctuations associated with the change in disorder realizations, and originate from the coherence between the natural channels of waves – the transmission eigenchannels.